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An untapped family of board game mechanics

Have you noticed how board games are in dire need of electoral reform?

No, wait, seriously. Hear me out. This makes sense.

In most board games, through a series of events, you acquire points (votes), where each point (vote) goes to at most one player, and then at the end the person with the most points (votes) wins outright, regardless of how narrow their margin is.

It’s literally plurality voting, and it leads to a number of the same problems.

One of those problems is that it amplifies small leads quite substantially. e.g. take Scrabble. I play a lot of Scrabble because it’s more or less our family game. I also win a lot of Scrabble. Sometimes comfortably if I managed to get that second bingo out, but often by fairly small margins – 10-20 points in a 300-400 point game is not a large victory, but with plurality victory that doesn’t matter, it’s still a victory.

It also creates spoiler effects, where you have players who obviously can’t win but still participate in pile-ons to people in the lead. e.g. if you’ve ever played a Steve Jackson game (Munchkin, Illuminati, etc) you’ve probably seen this in action – “They’re about to win! Get them!”.

Certainly not all games match this description: e.g. you get a lot of games where rather than scoring points there is a defined victory condition – war games where you take a rather different view of politics and must kill all your opponents (e.g. Risk), or hidden mission games where you must achieve some specific goal unknown to the others (e.g. Chrononauts). I’ll consider that sort of game out of scope here.

Some games you play until someone has hit some defined score and then they immediately win (e.g. Love Letter). This is a bit like majoritarian vote systems (where you only win if you get more than 50% of the vote), but not really.

So the analogy isn’t perfect, but I think it has enough merit for the games it applies to to be worth exploring how things can be different. If nothing else it might be an untapped source of interesting game mechanics.

Even within the scope of games which look like elections if you squint at them hard enough there’s some variation.

For example, I’m aware of at least one game which uses random ballot: Killer Bunnies and the Quest for the Magic Carrot.

In this game you acquire carrots (votes), then at the end of the game a winning carrot (vote) is drawn at random and the person who owns that carrot (had that vote cast for them) wins (is elected). So if you own 60% of the carrots then you have a 60% chance of winning.

The problem with random ballot in this context is both that Random Ballot isn’t great for presidential style single winner elections, and also that in the context of a game players (politicians) matter more than carrots (voters). Voters have a right to be well represented in the decision of which politician eats them, carrots don’t.

If the game were very short it would probably be OK, but getting to the end of a long game and then having victory be decided by quite such a large amount of luck is rather frustrating. I think there are ways to fix it and make random ballot a fun game mechanism, but I also worry that it’s a bit too close to existing scoring mechanisms and where it produces different answers players will mostly find it frustrating.

So instead I’d like to look at how you could use an entirely different class of electoral system to produce this effect: Condorcet systems.

The idea of a Condorcet system is that instead of focusing on point scoring you focus on pairwise victories: Which player beats which other player. If there is a player who beats every other player in a one on one victory, they are the Condorcet winner and win outright.

Depending on who you ask, electing the Condorcet winner is either a terrible or a great idea (my personal biases are “It depends what you’re electing them for but all else being equal the Condorcet winner is probably a pretty good choice”), but that doesn’t actually matter here, because the question is not whether it’s a great election system but whether it leads to an interesting game design!

And I think it does.

When there is no Condorcet winner interesting things happen where you get rock-paper-scissors like events where the majority prefers A to B, B to C and C to A. These are called Condorcet cycles. In this case you need some sort of alternate rule to decide which player is most like the Condorcet winner (this can also happen if you get candidates who are tied because an equal number of people prefer each to the other, but you can avoid this possibility by just having an odd number of voters).

There are a wide variety of systems for deciding who the “most Condorcet” candidate is when there is no true Condorcet winner. These range from the very simple to the very complicated, but there’s a particularly simple Condorcet system that I think is very suitable for game design.

It works as follows: You pick an incumbent (usually at random). Then every other candidate (player) challenges the incumbent in some order (usually random). If the majority strictly prefers them (they beat them according to some as of yet unspecified mechanism) then the incumbent drops out and the challenger becomes the incumbent, else the challenger drops out. Once all but one candidate has dropped out, the remaining incumbent is the winner.

There are a number of free variables in how you could turn this into a game mechanic:

Who gets to be starting incumbent?

What determines who wins in a head on head fight?

What order do people challenge in?

Who wins ties?

However you pick these free variables though, I think it’s most interesting if you do this in such a way that allows the possibility of Condorcet cycles (if you don’t it’s really just another scoring system). In order to do this you need something that looks like at least three voters.

The easiest way to do this is might be something like the following:

The game consists of resource acquisition in some manner. You have three resources and treat each as a vote. Each resource is claimed by whichever of the two players owns strictly more of it. If either player claims more resources than the other, that player wins. Otherwise, apply some tie breaking procedure.

Starting from that concept, you can elaborate itinto a full game. The following is a toy game that might work well (but probably would need significant refining through play testing) based this. It’s called “The King is Dead!”

The king is on his death bed and has no natural heir. He has named one, but the nobles are competing to change his mind, and regardless of who he chooses they might not last long enough to take the throne.

There are a few key nobles who might win, but their chances of victory are slim without the support of the two key factions of the kingdom: The peasants, and the clergy. The nobles must use their influence at court to curry favour with these two factions, but be careful! If you use all your influence outside the court, there may be no-one left to support you when you fall afoul of court intrigue.

Game setup:

An heir is picked at random from the players.

Three cards per player are drawn from a larger deck and are shuffled together to form the issue deck.

Each player is given twelve influence tokens.

Each issue card has a number of clergy points and a number of peasant points on it. It may also have a crown on it

The game is played in rounds which proceed as follows:

A card from the top of the deck is revealed.

The card is now auctioned off with an English auction: The heir bids zero on the card and then play proceeds clockwise, with each player either placing a higher bid or dropping out. Once everyone has dropped out except for the last bidder, that bidder gets that card, places it in front of them, and puts their bid in the centre temporarily.

If the card had a crown on it, the person who won it now becomes heir.

The bid is now redistributed amongst the players: One token at a time, starting from the heir (the new one if it changed places!) and proceeding clockwise until all the tokens have been redistributed

This process completes until the deck is out of cards. The king then dies, and a swift but bloody war of succession occurs.

Starting to the left of the current heir and proceeding clockwise, each player (not counting the player who was heir when the king died) gets the opportunity to challenge the current heir.

A challenge pits the two players against each other as follows:

Each player accrues a victory on each of three scores: Their total support from the peasantry, their total support from the clergy, and their total influence. If one player has a higher score than the other on each of these, they get a victory.

If one of the two has more victories than the other, that player wins. If they are tied, the current heir wins.

Whichever player won is now the new heir. If there are any more challengers left, the next challenger steps up and challenges the heir, otherwise they win and are crowned. Long live the king!

This game definitely needs play-testing and will almost certainly have a number of problems with it, but I think it’s an interesting corner of game design that I haven’t seen anything much like before.

The thing I like about it is also that it creates a much more interesting victory dynamic in most cases: In the case where someone wins really decisively then they still cream everybody else, but the back and forth between the three resources more or less guarantees that nobody will be a Condorcet winner unless everyone else played really badly – the more they spent to get that faction support, the more influence they gave to other players that they could use to claim some other support. This makes things tense right up until the end game.

More generally, I think there’s a rich seam of game design ideas in electoral theory that hasn’t been tapped much. There’s a theorem that says that almost any voting system admits tactical voting. For electoral system design this is a real pain, because systems which encourage tactical voting have a number of problems, but for game design it’s perfect because it means that there’s this giant body of well studied and powerful mechanics that are full of opportunities for tactical play.

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